A Common Root

Algebra Level 3

There are three real values of b for which the equations:

\(2{ x }^{ 2 }+5x+2b=0\) and \(2{ x }^{ 3 }+7{ x }^{ 2 }+5{ x }+1=0\) have at least one common root.

The sum of these three values for b can be expressed in the form \(\frac { m }{ n } \), where m and n are coprime positive integers.

Find \(m+n\).

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